Louis Yudowitz: Constructing a New Ancient Solution to Mean Curvature Flow by Stacking Pancakes

Ancient solutions to geometric flows, such as mean curvature flow, often arise as blow-up limits of singularities. Moreover, ancient solutions typically possess symmetries or positive curvature as a byproduct of the diffusion effects of the flow. Outside of the context of singularity analysis, ancient solutions form a very interesting, yet currently poorly understood, class of manifolds. In this talk, I will discuss a new construction of certain "collapsed" ancient solutions resulting from stacking ancient "pancakes", which were previously constructed by Bourni-Langford-Tinaglia. This stacked solution will be shown to have \(O(n)\times \Z_2\) symmetry, and I will also discuss constructing stacks with less (or no) symmetry. This is all based on an ongoing project with Mat Langford and Alex Mramor.